Answer: In general, over watering is usually followed by yellowing leaves that turn black at the tips and edges. Keeping your jasmine consistently watered will prevent this from happening.
Sometimes the tips or sides of a jasmine's leaves will appear brown. This usually happens after it has suffered a dry spell or when it goes through a period where, for whatever reason, the roots were not absorbing moisture well and then the plant suddenly gets a good watering. When cells in the leave's tips suddenly take on water, they literally swell up and burst. What you're seeing with the brown tips is actually dead plant tissue where the cells burst. This kind of browning can also happen to plants when they are initially transplanted and are suddenly given a heavy dose of water.
Hope this sheds some light on the problem.
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